JOURNAL BROWSE
Search
Advanced SearchSearch Tips
CONFORMAL VECTOR FIELDS AND TOTALLY UMBILIC HYPERSURFACES
facebook(new window)  Pirnt(new window) E-mail(new window) Excel Download
 Title & Authors
CONFORMAL VECTOR FIELDS AND TOTALLY UMBILIC HYPERSURFACES
Kim, Dong-Soo; Kim, Seon-Bu; Kim, Young-Ho; Park, Seong-Hee;
  PDF(new window)
 Abstract
In this article, we show that if a semi-Riemannian space form carries a conformal vector field V of which the tangential part on a connected hypersurface ecomes a conformal vector field and the normal part on does not vanish identically, then is totally umbilic. Furthermore, we give a complete description of conformal vector fields on semi-Riemannian space forms.
 Keywords
totally umbilic hypersurface;space form;conformal vector field;
 Language
English
 Cited by
1.
SPACES OF CONFORMAL VECTOR FIELDS ON PSEUDO-RIEMANNIAN MANIFOLDS,;;

대한수학회지, 2005. vol.42. 3, pp.471-484 crossref(new window)
1.
Infinitesimal rigidity of hyperquadrics in semi-Euclidean space, International Journal of Geometric Methods in Modern Physics, 2016, 13, 02, 1630001  crossref(new windwow)
2.
On the umbilicity of complete constant mean curvature spacelike hypersurfaces, Mathematische Annalen, 2014, 360, 3-4, 555  crossref(new windwow)
3.
Characterizing spheres by an immersion in Euclidean spaces, Arab Journal of Mathematical Sciences, 2017, 23, 1, 85  crossref(new windwow)
4.
On the Gauss mapping of hypersurfaces with constant scalar curvature in ℍ n+1, Bulletin of the Brazilian Mathematical Society, New Series, 2014, 45, 1, 117  crossref(new windwow)
5.
On the Gauss map of Weingarten hypersurfaces in hyperbolic spaces, Bulletin of the Brazilian Mathematical Society, New Series, 2016, 47, 4, 1051  crossref(new windwow)
6.
Characterizations of immersed gradient almost Ricci solitons, Pacific Journal of Mathematics, 2017, 288, 2, 289  crossref(new windwow)
 References
1.
J. Korean Math. Soc., 1996. vol.33. pp.507-512

2.
Nagoya Math. J., 1974. vol.55. pp.1-3

3.
Quart. J. Math. Oxford(2), 1985. vol.36. pp.1-15 crossref(new window)

4.
Geometry of submanifolds and its applications, 1981.

5.
Total mean curvature and submanifolds of finite type, 1984.

6.
Symmetries of Spacetime and Riemannian Manifolds, 1999.

7.
Diff. Geom. and Appl., 1991. vol.1. pp.35-45 crossref(new window)

8.
J. Diff. Geom., 1976. vol.11. pp.547-571

9.
Thesis, 1988.

10.
Class. Quantum Grav., 1991. vol.8. pp.819-825 crossref(new window)

11.
Transformation groups in differential geometry, 1972.

12.
J. Math. Pures et Appl., 1995. vol.74. pp.453-481

13.
Diff. Geom. and Appl., 1997. vol.7. pp.237-250 crossref(new window)

14.
Semi-Riemannian geometry with application to relativity, 1983.

15.
Cambridge monographs on Math. Physics, 1987. vol.1;2.

16.
Differential geometric structures, 1981.

17.
C. R. Math. Rep. Acad. Sci. Canada, 1985. vol.7. pp.201-205

18.
J. Math. Soc. Japan, 1967. vol.19. pp.328-346 crossref(new window)

19.
The theory of Lie derivatives and its applications, 1957.